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11
The Exact Computation Paradigm
, 1994
"... We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next ..."
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Cited by 97 (10 self)
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We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original massproduced computers were pocket calculators. Although one's first exposure to computers today is likely to be some nonnumerical application, numeri...
Computing Roadmaps of General SemiAlgebraic Sets
, 1993
"... In this paper we study the problem of determining whether two points lie in the same connected component of a semialgebraic set S. Although we are mostly concerned with sets S # , our algorithm can also decide if points in an arbitrary set S # R can be joined by a semialgebraic path, for any real ..."
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Cited by 50 (2 self)
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In this paper we study the problem of determining whether two points lie in the same connected component of a semialgebraic set S. Although we are mostly concerned with sets S # , our algorithm can also decide if points in an arbitrary set S # R can be joined by a semialgebraic path, for any real closed field R. Our algorithm computes a onedimensional semialgebraic subset ##S# of S (actually of an embedding of S in a space R for a certain real extension field R of the given field R#. ##S# is called the roadmap of S. The basis of this work is the roadmap algorithm described in [3], [4] whichworked only for compact, regularly stratified sets. We measure...
Topological Queries in Spatial Databases
 Journal of Computer and System Sciences
, 1996
"... We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invar ..."
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Cited by 44 (2 self)
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We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invariant characterizing semialgebraic regions up to homeomorphism. All topological queries on semialgebraic regions can be answered by queries on the invariant whose complexity is polynomially related to the original. Also, we show that for the purpose of answering topological queries, semialgebraic regions can always be represented simply as polygonal regions. We then study query languages for topological properties of twodimensional spatial databases, starting from the topological relationships between pairs of planar regions introduced by Egenhofer. We show that the closure of these relationships under appropriate logical operators yields languages which are complete for topological prope...
Automatic construction of simple artifactbased workflows
 In: Proc. of the 12th Int. Conf. on Database Theory (ICDT 2009
, 2009
"... Almost all medium and largescale businesses rely on electronic workflow systems to manage their business processes. A key challenge is to enable the easy reuse and modification of these workflow schemas and their pieceparts, so that they can be adapted to new business situations. This paper desc ..."
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Cited by 26 (2 self)
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Almost all medium and largescale businesses rely on electronic workflow systems to manage their business processes. A key challenge is to enable the easy reuse and modification of these workflow schemas and their pieceparts, so that they can be adapted to new business situations. This paper describes an approach for automatic construction (and thus, evolution) of a workflow schema that satisfies a specified condition (or “goal”), starting from a set of basic building block services (or “tasks”). We use a workflow model based on “business artifacts”, which represent key (real or conceptual) business entities, and include both the businessrelevant data about them and a specification of their lifecycle, that is, how they can evolve over time as they move through the workflow as the result of services being applied to them. This paper uses a declarative form of artifactcentric workflow. The
Querying Spatial Databases via Topological Invariants
 In PODS'98
, 1998
"... The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered ..."
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Cited by 17 (2 self)
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The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered are firstorder on the spatial database side, and fixpoint + counting, fixpoint, and firstorder on the topological invariant side. In particular, it is shown that fixpoint + counting expresses precisely all the ptime queries on topological invariants; if the regions are connected, fixpoint expresses all ptime queries on topological invariants. 1 Introduction Spatial data is an increasingly important part of database systems. It is present in a wide range of applications: geographic information systems, video databases, medical imaging, CADCAM, VLSI, robotics, etc. Different applications pose different requirements on query languages and therefore on the kind of spatial information th...
Computation of Equilibria in Noncooperative Games
 IN PROC. WORKSHOP FOR COMPUTABLE ECONOMICS
, 2000
"... This paper presents algorithms for finding equilibria of mixed strategy in multistage noncooperative games of incomplete information (like probabilistic blindfold chess, where at every opportunity a player can perform different moves with some probability). These algorithms accept input games in ..."
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Cited by 6 (1 self)
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This paper presents algorithms for finding equilibria of mixed strategy in multistage noncooperative games of incomplete information (like probabilistic blindfold chess, where at every opportunity a player can perform different moves with some probability). These algorithms accept input games in extensive form. Our main result is an algorithm for computing Sequential equilibrium, which is the most widely accepted notion of equilibrium (for mixed strategies of noncooperative probabilistic games) in mainstream economic game theory. Previously, there were no known algorithms for computing sequential equilibria strategies (except for the special case of single stage games). The computational aspects of passage from a recursive presentation of a game to its extensive form are also discussed. For nontrivial inputs the concatenation of this procedure with the equilibrium computation is time intensive, but has low spatial requirements. Given a recursively represented game, with a po...
Computing the Newtonian graph
 J. Symbolic Comput
, 1997
"... In his study of Newton's root approximation method, Smale (1985) de ned the Newtonian graph of a complex univariate polynomial f. The vertices of this graph are the roots of f and f 0 and the edges are the degenerate curves of ow of the Newtonian vector eld Nf (z) =;f(z)=f 0 (z). The embedded e ..."
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Cited by 4 (0 self)
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In his study of Newton's root approximation method, Smale (1985) de ned the Newtonian graph of a complex univariate polynomial f. The vertices of this graph are the roots of f and f 0 and the edges are the degenerate curves of ow of the Newtonian vector eld Nf (z) =;f(z)=f 0 (z). The embedded edges of this graph form the boundaries of root basins in Newton's root approximation method. The graph de nes a treelike relation on the roots of f and f 0, similar to the linear order when f has only real roots. We give an e cient algebraic algorithm based on cell decomposition to compute the Newtonian graph. The resulting structure can be used to query whether two points in C are in the same basin. This gives us a modi ed version of Newton's method in which one can test whether a step has crossed a basin boundary. Stefansson (1995) has recently extended this algorithm to handle rational and algebraic functions without signi cant increase in complexity. He has shown that the Newtonian graph tesselates the associated Riemann surface and can be used in conjunction with Euler's formula to give anNC algorithm to calculate the genus of an algebraic curve. 1.
Exploration of Geographic Databases: Supporting a Focus+Context Interaction Style
 JOURNAL OF APPLIED SYSTEM STUDIES
, 2001
"... ..."
Lower Bounds for Shortest Path and Related Problems
 In Proc. 28th Ann. IEEE
, 1987
"... We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of ..."
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Cited by 1 (0 self)
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We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We first apply the method to the shortest path problem in three dimensions. The problem is to find the shortest path under an L p metric (e.g. a euclidean metric) between two points amid polyhedral obstacles. Although this problem has been extensively studied, there were no previously known lower bounds. We show that there may be exponentially many shortest path classes in singlesource multipledestination problems, and that the singlesource singledestination problem is NPhard. We use a similar proof technique to show that two dimensional dynamic motion planning with bounded velocity is NPhard. Finally we extend the technique to compliant motion planni...
A General Strategy for Decomposing Topological Invariants of Spatial Databases and an Application
, 2001
"... Topological invariants of spatial databases (i.e., nite structures that capture the topological properties of the database) are receiving increasing attention since they can act as a basic structure to tackle relevant problems in the eld (e.g., assessment of the topological equivalence). In this p ..."
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Topological invariants of spatial databases (i.e., nite structures that capture the topological properties of the database) are receiving increasing attention since they can act as a basic structure to tackle relevant problems in the eld (e.g., assessment of the topological equivalence). In this paper, the novel notion of boundary decomposition of a topological invariant is introduced and a polynomial time algorithm to compute such a decomposition is given. The decomposition consists of a recursive subdivision of the topological invariant into a nite set of simpler structures, each being a topological invariant in itself. The decomposition is proved to be lossless, a nice property which makes the boundary decomposition useful in real applications. As a relevant application, we use the boundary decomposition as the basis for devising a polynomial time algorithm for testing the topological equivalence of two 2dimensional spatial databases.